Conditional formats

[Brendan Zabarauskas]

It would be useful to have format descriptions that are refine other formats with predicates:

{ x <- f | e }

For example, in OpenType we might see something like:

{ sfnt_version <- u32be | sfnt_version == 0x00010000 || sfnt_version == "OTTO" }

Rough specification

The typing rules for the core language could look something like:

  f : Format     x : Repr Format ⊢ e : Bool
──────────────────────────────────────────────
           { x <- f | e } : Format


Repr { x <- f | e } = Repr f


  s .. s' : f ⟹ e₁   x : Repr f = e₁ ⊢ e₂ = true : Bool
────────────────────────────────────────────────────────────
          s .. s' : { x <- f | e₂ } ⟹ e₁

• { x <- f | e } is a Format when:
  • f is a Format
  • assuming x : Repr Format, e is a Bool
• the representation of { x <- f | e } is Repr f
• the bit sequence s .. s' is recognized with { x <- f | e₂ } as an expression e₁ when:
  • the bit sequence s .. s' is recognized with f as an expression e₁
  • assuming x : Repr f = e₁, e₂ is the same Bool as true

Elaborated typing rules

---

Some might find it easier to read these rules with explicit typing contexts, Γ:

  Γ ⊢ f : Format     Γ, x : Repr Format ⊢ e : Bool
────────────────────────────────────────────────────
           Γ ⊢ { x <- f | e } : Format

• under the context Γ, { x <- f | e } is a Format when:
  • under the context Γ, f is a Format
  • under the context Γ, x : Repr Format, e is a Bool

---

Note: The binary interpretation uses a similar notation as Mark Brown in the prolog prototype.

Naming ideas

Some alternative names for these format descriptions could be:

• conditional formats
• refinement formats
• guard formats

Future extensions

Predicate preservation

Eventually we could preserve the guard condition in the representation types, using refinement types:

-   f : Format     x : Repr Format ⊢ e : Bool
+   f : Format     x : Repr Format ⊢ e : Prop
  ──────────────────────────────────────────────
             { x <- f | e } : Format


- Repr { x <- f | e } = Repr f
+ Repr { x <- f | e } = { x : Repr f | e }

Syntactic Sugar

We could eventually add some sugar for record formats:

{
    sfnt_version <- u32be == 0x00010000 || "OTTO",
    ...
}

Or perhaps:

{
    sfnt_version <- u32be if sfnt_version == 0x00010000 || sfnt_version == "OTTO",
    ...
}